Predicting skull loading: applying multibody dynamics analysis to a macaque skull.

Lizard skulls vary greatly in shape and construction, and radical changes in skull form during evolution have made this an intriguing subject of research. The mechanics of feeding have surely been affected by this change in skull form, but whether this is the driving force behind the change is the underlying question that we are aiming to address in a programme of research. Here we have implemented a combined finite element analysis (FEA) and multibody dynamics analysis (MDA) to assess skull biomechanics during biting. A skull of Uromastyx hardwickii was assessed in the present study, where loading data (such as muscle force, bite force and joint reaction) for a biting cycle were obtained from an MDA and applied to load a finite element model. Fifty load steps corresponding to bilateral biting towards the front, middle and back of the dentition were implemented. Our results show the importance of performing MDA as a preliminary step to FEA, and provide an insight into the variation of stress during biting. Our findings show that higher stress occurs in regions where cranial sutures are located in functioning skulls, and as such support the hypothesis that sutures may play a pivotal role in relieving stress and producing a more uniform pattern of stress distribution across the skull. Additionally, we demonstrate how varying bite point affects stress distributions and relate stress distributions to the evolution of metakinesis in the amniote skull.

Evaluation of crack tip stress and strain fields under nonproportional loading in a viscoelastic material

Numerous anthropological studies have been aimed at estimating jaw-adductor muscle forces, which, in turn, are used to estimate bite force. While primate jaw adductors show considerable intra- and intermuscular heterogeneity in fibre types, studies generally model jaw-muscle forces by treating the jaw adductors as either homogeneously slow or homogeneously fast muscles. Here, we provide a novel extension of such studies by integrating fibre architecture, fibre types and fibre-specific tensions to estimate maximum muscle forces in the masseter and temporalis of five anthropoid primates: Sapajus apella (N = 3), Cercocebus atys (N = 4), Macaca fascicularis (N = 3), Gorilla gorilla (N = 1) and Pan troglodytes (N = 2). We calculated maximum muscle forces by proportionally adjusting muscle physiological cross-sectional areas by their fibre types and associated specific tensions. Our results show that the jaw adductors of our sample ubiquitously express MHC α-cardiac, which has low specific tension, and hybrid fibres. We find that treating the jaw adductors as either homogeneously slow or fast muscles potentially overestimates average maximum muscle forces by as much as approximately 44%. Including fibre types and their specific tensions is thus likely to improve jaw-muscle and bite force estimates in primates.

The purposes of the study were to establish isometric torque reference values for healthy 6- to 8-year-old children for 6 lower extremity muscles and determine the effects of gender, age, height, weight, and physical activity upon strength. A hand-held dynamometer was used to obtain force/torque values for 154 children. Age-referenced force/torque and cutoff values are provided for each muscle group. Torque increased with age and height for all muscles and with weight for all muscles except knee extensors. No gender differences were found. Children who participated in 3 or more hours per week in organized sports were stronger in 4 of 6 muscles; the number of hours spent in active play did not affect torque. This study provides hand-held dynamometer strength reference values to enable clinicians to determine if clients of the same age, height, and weight have muscle weakness.

A complete experimental determination of the stress and strain fields in an arbitrary deformed structure is generally unavailable. However, for two dimensional elasticity problems, such determinations are possible since in those cases one needs only to solve for three stresses (two normal and one shear). In fact, such determinations have been conducted quite often. By using isochromatic and isoclinic photoelastic data, the shear difference and numerical iteration techniques (1) and the least squares techniques (2) have been successfully used for complete stress field determinations of two dimensional elasticity problems. Though the shear difference technique can be particularly sensitive to cumulative errors resulting from numerical integration, the least squares technique is not affected by this and appears to yield better accuracy. The methods just cited use both experimental data and one or more mechanics conditions(e.g., the equations of equilibrium) to determine the stress field. However, the stress field can also be obtained from experimental data alone for planar elasticity problems, if there is enough of it to solve for the three stresses. For example, the Moire* technique or the combination of isochromatic, isoclinic, and isopachic data (for transparent models) can be used for such determinations. Further, with the marriage of advanced image processing equipment to computers, such analyses using this type of data can be conveniently conducted. It is even possible that such analyses could be more accurate than those using the combined experimental/numerical techniques cited above. The purposes of this report are two fold: i) to describe a single apparatus for obtaining isochromatic, isopachic, and isoclinic results for complete stress field determinations of two dimensional transparent models, and ii) to compare experimental and theoretical stress field values for an antisymmetrically loaded beam obtained using that apparatus.© (1987) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Josephoartigasia monesi, from the Pliocene of Uruguay, is the largest known fossil rodent, with an estimated body mass of 1000 kg. In this study, finite element analysis was used to estimate the maximum bite force that J. monesi could generate at the incisors and the cheek teeth. Owing to uncertainty in the model inputs, a sensitivity study was conducted in which the muscle forces and orientations were sequentially altered. This enabled conclusions to be drawn on the function of some of the masticatory muscles. It was found that J. monesi had a bite of 1389 N at the incisors, rising to 4165 N at the third molar. Varying muscle forces by 20% and orientations by 10° around the medio-lateral aspect led to an error in bite force of under 35% at each tooth. Predicted stresses across the skull were only minimally affected by changes to muscle forces and orientations, but revealed a reasonable safety factor in the strength of the skull. These results, combined with previous work, lead us to speculate that J. monesi was behaving in an elephant-like manner, using its incisors like tusks, and processing tough vegetation with large bite forces at the cheek teeth.

Data-model coupling driven stress field measurements

The lepidosaurian skull has long been of interest to functional morphologists and evolutionary biologists. Patterns of bone loss and gain, particularly in relation to bars and fenestrae, have led to a variety of hypotheses concerning skull use and kinesis. Of these, one of the most enduring relates to the absence of the lower temporal bar in squamates and the acquisition of streptostyly. We performed a series of computer modeling studies on the skull of Uromastyx hardwickii, an akinetic herbivorous lizard. Multibody dynamic analysis (MDA) was conducted to predict the forces acting on the skull, and the results were transferred to a finite element analysis (FEA) to estimate the pattern of stress distribution. In the FEA, we applied the MDA result to a series of models based on the Uromastyx skull to represent different skull configurations within past and present members of the Lepidosauria. In this comparative study, we found that streptostyly can reduce the joint forces acting on the skull, but loss of the bony attachment between the quadrate and pterygoid decreases skull robusticity. Development of a lower temporal bar apparently provided additional support for an immobile quadrate that could become highly stressed during forceful biting.

Dynamic crack growth along elastic bimaterial interfaces have been studied extensively in the past decade by many researchers. In contrast, studies of dynamic interfacial fracture under elastic-plastic conditions are still very limited. In this presentation, the results of an analytic investigation of the asymptotic stress and deformation fields at the tip of a dynamically growing interface crack between a ductile material and a rigid substrate under plane stress conditions will be reported. The ductile material is taken to be ideally plastic and obey the J2 flow theory of plasticity. Under steady-state conditions, the asymptotic structure of the crack-tip stress, velocity and strain fields has been obtained. The study reveals that two types of crack-tip sectors exist, namely uniform and nonuniform plastic sectors and that the stress, strain and velocity fields are bounded in all sectors. In a uniform sector, the rectangular Cartesian components of the stress, strain and velocity fields are constant, and there is no plastic strain accumulation. In a nonuniform sector, the stress, strain and velocity components at a point depend on the angular position of the point in the crack-tip polar coordinate system and are governed by a system of simultaneous ordinary differential equations. This is a sector where plastic strains can accumulate. A general crack-tip sector assembly has been obtained for a practical range of crack growth speeds. Several nontrivial families of admissible solutions of the crack-tip fields based on this general assembly of uniform and nonuniform crack-tip sectors will be presented and discussed. Finally, comparisons with corresponding plane strain solutions (Deng, 1993 a) will be made.

When crack tip constraint is high, the crack tip contour integral J characterises the asymptotic stress, strain and displacement fields of a stationary crack in an elastic-plastic material. In other cases, the crack tip fields can be related to J and a second parameter Q which governs the crack tip constraint. These observations are the basis of J-Q fracture mechanics assessments. In the most usual procedure J is compared to an effective, constraint-corrected fracture toughness Jc which is derived from Q and the fracture toughness of the material. The difference Jc – J is a measure of the margin of safety. The assessment procedure assumes there are no initial inelastic strains in the component or the fracture toughness specimen prior to introducing the crack and subsequent loading. However, plant components may contain inelastic strains prior to cracking arising from welding and other manufacturing or fit-up processes. This initial strain field can be established by a finite element analysis that simulates the welding and/or manufacture sequence. Weld residual stresses develop due to the accumulation of incompatible, inelastic strains, including thermal, plastic and transformation strains in the material. If a crack is inserted into an initial strain field, a procedure is required to calculate J by analysis of the resulting crack tip fields. Moreover, for the fracture assessment method to remain valid, it must be demonstrated that the values of J and Q continue to govern the onset of crack extension or fracture so that a meaningful comparison of J with Jc can be made. This paper describes a domain integral for calculating J when inelastic strains exist prior to cracking, and its implementation in the JEDI computer code. The code is used to determine J for a crack inserted into a three-point bend specimen containing an initial inelastic strain field representative of one that might develop during welding. The extent to which the crack tip stress field is characterised by J and Q is examined by comparing it to the field for high constraint, small-scale yielding conditions.

Contemporary stress and strain field in the Mediterranean from stress inversion of focal mechanisms and GPS data

This study determines the influence law of the maximum eccentric uncoupling coefficient on the pressure field distribution at the hole wall through theoretical analysis to investigate the time-varying effect of the maximum eccentric uncoupling coefficient on the stress field of an eccentric charge structure. The findings from the theoretical analysis indicate that when the maximum eccentric uncoupling coefficient (K) is 1, the pressure at the ring hole wall exhibits a circular distribution. As K increases, the pressure distribution at the ring hole wall becomes elliptical, with the elliptical eccentricity increasing progressively. This research employs an ultra-high-speed digital imaging system to assess the impact of the maximum eccentric uncoupling coefficient on the attenuation pattern of the stress field within the elastic vibration region. The results demonstrate that the eccentric charge structure’s effect on the strain field is predominantly observed in its time and strength effects. This is evident in the strain field’s time delay on the non-eccentric side and the fact that the strain field’s strength on this side is weaker than on the eccentric side. In the elastic vibration region, the primary type of radial stress is compressive, whereas the circumferential stress is chiefly tensile. As the measurement point’s distance increases, the peak values of both radial compressive and circumferential tensile stresses diminish exponentially. Interestingly, the attenuation index of the radial stress is notably lower than that of the circumferential stress. The change in the K value has a minimal impact on the attenuation indices of both radial and circumferential stresses. At equal distances from the eccentric side, the peak values of both radial and circumferential stresses display a consistent pattern with K and a linear pattern at distances from the eccentric side and in symmetry. The stress field’s intensity and attenuation pattern on the eccentric side remain largely unaffected by variations in K. Conversely, the stress field attenuation on the non-eccentric side is significantly influenced by K value changes, as is the symmetric side.

A non-axisymmetric cylinder with an oblique flange has broad application prospects. Spinning is the main production process for this kind of workpiece. Finite element modeling is a necessary method to study some key problems that are difficult to be solved merely through experiments, such as the strain and stress fields in the development of this spinning technology. In this study, the spinning process of a non-axisymmetric oblique flange cylindrical part was established and simulated using ABAQUS/explicit software. The credibility of the simulation result was validated through an experiment. The influence of the axial roller feed along the cylinder wall on the distribution of wall thickness and stress and strain during the forming process was analyzed. The change in stress field and strain field with time was analyzed, and the quantitative relationship between forming conditions and forming results was described. Furthermore, the forming principle of the flange was analyzed. It would be beneficial for flange forming to reduce the increasing distance of the cylinder wall in the 180° direction (parameter c) and the vertical distance from the closest point to the spindle as the roller returns back in the 180° direction (parameter d), to a certain extent. Hence, a workpiece with an ideal appearance was obtained. By comparing the wall thickness distribution, the design and optimization of the roller path were once again verified to be reasonable.

This paper considers a rectangular Volterra dislocation loop lying beneath and parallel to a free surface in a semi-infinite material. The paper utilizes the displacement field of an infinitesimal dislocation loop to obtain the strain field and then integrate over a finite rectangular area. For the loop, it can have three non-zero Burgers vector components. The stress field is also obtained from Hooke’s law for isotropic materials. Analytical and numerical verifications of the strain and stress fields are performed. In addition, the effect of the free surface on stresses is displayed versus depth from the surface. Verification includes satisfaction of the zero-traction boundary condition, the stress equilibrium equations and the strain compatibility equations.

Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity